--- a/src/HOL/Integ/cooper_proof.ML Fri Aug 06 17:07:04 2004 +0200
+++ b/src/HOL/Integ/cooper_proof.ML Fri Aug 06 17:19:50 2004 +0200
@@ -17,7 +17,8 @@
val qe_exI : thm
val list_to_set : typ -> term list -> term
val qe_get_terms : thm -> term * term
- val cooper_prv : Sign.sg -> term -> term -> thm
+ val cooper_prv : Sign.sg -> term -> term -> thm
+ val cooper_prv2 : Sign.sg -> term -> term -> thm
val proof_of_evalc : Sign.sg -> term -> thm
val proof_of_cnnf : Sign.sg -> term -> (term -> thm) -> thm
val proof_of_linform : Sign.sg -> string list -> term -> thm
@@ -792,8 +793,8 @@
((if (f ((dest_numeral s),(dest_numeral t)))
then prove_elementar sg "ss" (HOLogic.mk_eq(at,HOLogic.true_const))
else prove_elementar sg "ss" (HOLogic.mk_eq(at, HOLogic.false_const)))
- handle _ => instantiate' [Some cboolT] [Some (cterm_of sg at)] refl
- | _ => instantiate' [Some cboolT] [Some (cterm_of sg at)] refl ))
+ handle _ => instantiate' [Some cboolT] [Some (cterm_of sg at)] refl)
+ | _ => instantiate' [Some cboolT] [Some (cterm_of sg at)] refl )
|Const("Not",_)$(Const (p,_) $ s $ t) =>(
case assoc (operations,p) of
Some f =>
@@ -920,6 +921,64 @@
end
|cooper_prv _ _ _ = error "Parameters format";
+(* ********************************** *)
+(* cooper_prv2 is just copy and paste *)
+(* And only generates proof with *)
+(* bset and minusinfity *)
+(* ********************************** *)
+
+
+
+fun cooper_prv2 sg (x as Free(xn,xT)) efm = let
+ (* lfm_thm : efm = linearized form of efm*)
+ val lfm_thm = proof_of_linform sg [xn] efm
+ (*efm2 is the linearized form of efm *)
+ val efm2 = snd(qe_get_terms lfm_thm)
+ (* l is the lcm of all coefficients of x *)
+ val l = formlcm x efm2
+ (*ac_thm: efm = efm2 with adjusted coefficients of x *)
+ val ac_thm = [lfm_thm , (proof_of_adjustcoeffeq sg x l efm2)] MRS trans
+ (* fm is efm2 with adjusted coefficients of x *)
+ val fm = snd (qe_get_terms ac_thm)
+ (* cfm is l dvd x & fm' where fm' is fm where l*x is replaced by x*)
+ val cfm = unitycoeff x fm
+ (*afm is fm where c*x is replaced by 1*x or -1*x *)
+ val afm = adjustcoeff x l fm
+ (* P = %x.afm*)
+ val P = absfree(xn,xT,afm)
+ (* This simpset allows the elimination of the sets in bex {1..d} *)
+ val ss = presburger_ss addsimps
+ [simp_from_to] delsimps [P_eqtrue, P_eqfalse, bex_triv, insert_iff]
+ (* uth : EX x.P(l*x) = EX x. l dvd x & P x*)
+ val uth = instantiate' [] [Some (cterm_of sg P) , Some (cterm_of sg (mk_numeral l))] (unity_coeff_ex)
+ (* e_ac_thm : Ex x. efm = EX x. fm*)
+ val e_ac_thm = (forall_intr (cterm_of sg x) ac_thm) COMP (qe_exI)
+ (* A and B set of the formula*)
+ val B = bset x cfm
+ val A = []
+ (* the divlcm (delta) of the formula*)
+ val dlcm = mk_numeral (divlcm x cfm)
+ (* Which set is smaller to generate the (hoepfully) shorter proof*)
+ val cms = "mi"
+ (* synthesize the proof of cooper's theorem*)
+ (* cp_thm: EX x. cfm = Q*)
+ val cp_thm = cooper_thm sg cms x cfm dlcm A B
+ (* Exxpand the right hand side to get rid of EX j : {1..d} to get a huge disjunction*)
+ (* exp_cp_thm: EX x.cfm = Q' , where Q' is a simplified version of Q*)
+ val exp_cp_thm = refl RS (simplify ss (cp_thm RSN (2,trans)))
+ (* lsuth = EX.P(l*x) ; rsuth = EX x. l dvd x & P x*)
+ val (lsuth,rsuth) = qe_get_terms (uth)
+ (* lseacth = EX x. efm; rseacth = EX x. fm*)
+ val (lseacth,rseacth) = qe_get_terms(e_ac_thm)
+ (* lscth = EX x. cfm; rscth = Q' *)
+ val (lscth,rscth) = qe_get_terms (exp_cp_thm)
+ (* u_c_thm: EX x. P(l*x) = Q'*)
+ val u_c_thm = [([uth,prove_elementar sg "ss" (HOLogic.mk_eq (rsuth,lscth))] MRS trans),exp_cp_thm] MRS trans
+ (* result: EX x. efm = Q'*)
+ in ([e_ac_thm,[(prove_elementar sg "ss" (HOLogic.mk_eq (rseacth,lsuth))),u_c_thm] MRS trans] MRS trans)
+ end
+|cooper_prv2 _ _ _ = error "Parameters format";
+
(* **************************************** *)
(* An Other Version of cooper proving *)